ASYMMETRIC CRITICAL FRACTIONAL p-LAPLACIAN PROBLEMS

We consider the asymmetric critical fractional p-Laplacian problem (-Delta)(p)(s)u = lambda vertical bar u vertical bar(p-2)u + u(+)(s)(p)*-1 , in Omega; u = 0, in R-N \ Omega; where lambda > 0 is a constant, p(s)* = Np/(N - sp) is the fractional critical Sobolev exponent, and u(+) (x) = max{u(x), 0}. This extends a result in the literature for the local case s = 1. We prove the theorem based on the concentration compactness principle of the fractional p-Laplacian and a linking theorem based on the Z(2)-cohomological index.